Submitted on August 11, 2007
Accepted on May 19, 2008
Analysis of Nonstationarity in Renal Autoregulation Mechanisms Using Time-Varying Transfer and Coherence Functions
Ki H. Chon1*, Yuru Zhong1, Leon C. Moore2, Niels-Henrik Holstein-Rathlou3, and William A Cupples4
1 Biomedical Engineering, SUNY at Stony Brook, Stony Brook, New York, United States
2 Department of Physiology and Biophysics, SUNY Health Science Center, Stony Brook, New York, United States
3 Department of Medical Physiology, The Panum Instititute, Copenhagen N, Denmark
4 Biology, University of victoria, Vancouver, Canada
* To whom correspondence should be addressed. E-mail: ki.chon{at}sunysb.edu.
The extent to which renal blood flow dynamics vary in time, and whether such variation contributes substantively to dynamic complexity, has emerged as an important question. Data from Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR) were analyzed by time-varying transfer functions (TVTF) and coherence functions (TVCF). Both TVTF and TVCF allow quantification of nonstationarity in the frequency ranges associated with the autoregulatory mechanisms. TVTF analysis shows that autoregulatory gain in SDR and SHR varies in time, and that SHR exhibit significantly more nonstationarity than SDR. TVTF gain in the frequency range associated with the myogenic mechanism was significantly higher in SDR than in SHR, but no statistical difference was found with tubuloglomerular (TGF) gain. Further, TVCF analysis revealed that the coherence in both strains is significantly nonstationary and that low-frequency coherence was negatively correlated with autoregulatory gain. TVCF in the frequency range from 0.1 to 0.3 Hz was significantly higher in SDR (7 out of 7 > 0.5) than in SHR (5 out of 6 < 0.5), and consistent for all time points. For TGF frequency range (0.03 to 0.05 Hz), coherence exhibited substantial nonstationarity in both strains. Five of 6 SHR had mean coherence < 0.5, while 4 of 7 SDR exhibited coherence < 0.5. Together, these results demonstrate substantial nonstationarity in autoregulatory dynamics in both SHR and SDR. Further, they indicate that the nonstationarity accounts for most of the dynamic complexity in SDR, but that it accounts for only a part of the dynamic complexity in SHR.
